7. The positive interval (s) of the functiony=-x ²1 are
Answers
Let's graph the function and find the positive intervals, as follows:
Therefore, the interval is : (-∞ , +-∞)
Related Questions
The graph below shows the profits for a circus.a. What is the dependent variable?b. What is the independent variable?c. What is the slope (rate of change) of the line?d. What does this number mean for the circus?
Answers
Most of the time, the independent variable is located in the horizontal axis (x) and the dependent variable is located in the vertical axis (y), a change in the independent variable causes an influence on the value of the dependent variable, in this case, the dependent variable would be the profit in $ (thousands) and the independent variable is the # of tickets sold (thousands).
The slope of a line (m) is calculated by means of the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are points of the line, i this case, the x coordinate of the line represents # of tickets sold and the y coordinate the profit in $.
We can take whatever point from the line, I'll take the points (0,0) and (40,60), then the slope of the line is:
[tex]m=\frac{60-0}{40-0}=\frac{60}{40}=\frac{6}{4}=\frac{3}{2}[/tex]Then, the slope of the line equals 3/2
The slope of this line represents the earnings per ticket
Bill paints murals. He recorded the total amount of white paint that he used for his murals each month in the table below. In April, Bill used 2/3 of the amount that he used in March. Fill in the amount of white paint Bill used in April in the table below.month liters of white paint usedMarch 4/5Aprilmay 1 1/4
Answers
Answer:
8/15 (in litres).
Explanation:
In April, Bill used 2/3 of the amount that he used in March.
[tex]\begin{gathered} \text{Amount used in April}=\frac{2}{3}\text{ of the amount used in March} \\ =\frac{2}{3}\times\frac{4}{5} \end{gathered}[/tex]Next, we simplify:
[tex]\begin{gathered} =\frac{2\times4}{3\times5} \\ =\frac{8}{15} \end{gathered}[/tex]The amount he used in April was 8/15 (in litres).
Which relation is a function?
Answers
Answer:
The V (Bottom left)
Step-by-step explanation:
The top left is NOT a function because it fails the vertical line test. In fact, it is a vertical line.
The top right is NOT a function because it also fails the vertical line test. This graph may be considered as an inverse of a different function but it will not be a true inverse.
The bottom left IS a function because it passes the vertical line test. It has 1 x value for every y value.
The bottom right is NOT a function because it fails the vertical line test. At most x values, it has 2 y values.
The vertical line test is an imaginary line that you draw to test a function. If only 1 point hits the vertical line, then it is a function. The vertical line can be placed at any point in the graph.
Hope that helps
help me pleaseeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer:
Domain: A, [tex][2, \infty)[/tex]
Range: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 2y = 5.
Answers
we need to find the equation of a like, in two different ways
a) slope-interceppt Y=mX+b
b) standard form aX+bY=c
the information we have is,
it's parallel to x+2y=5 (this mean the have the same slope
so, let's find it
x+2y=5
2y=5-x
y=5/2 - 1/2 x
the slope is m= -1/2
The other thing we know is the line passing through (-3,5)
so when x=-3 the value of Y has to be 5
So let's check, until now we have the slope, our line is y= -1/2x + B
let's find out the value of B, replacing the values of x and y
5= -1/2 * -3 +B
5= 3/2 + B
7/2= B
So, the answer to (a) is=
Y= -1/2 X + 7/2
b) we need to change from slope to standard form
Y= -1/2 X + 7/2
Y + 1/2 X= 7/2
i think that's standard form, but also you can divide for 7/2 to get
2/7 Y + 1/7 X = 1
Solve for x and y.
8
5
Х
15
У
12
Answers
From the first diagram, we can write the equation:
[tex]x\text{ + y = 16 ----equation(1)}[/tex]From the second diagram, we can write the equation:
[tex]8\text{ + y = x ------equation (2)}[/tex]Substitute the expression for x in equation (2) into equation (1)
[tex]\begin{gathered} x\text{ + y = 16} \\ 8\text{ + y + y = 16} \\ 8\text{ + 2y = 16} \\ \text{Collect like terms} \\ 2y\text{ = 16 -8} \\ 2y\text{ = 8} \\ \text{Divide both sides by 2} \\ \frac{2y}{2}\text{ = }\frac{8}{2} \\ y\text{ = 4} \end{gathered}[/tex]Substituting the value of y into equation (2):
[tex]\begin{gathered} 8\text{ + y = x} \\ x\text{ = 8 + 4} \\ x\text{ = 12} \end{gathered}[/tex]Answer:
x = 12, y = 4
A) Determine the equation of the parabola with a vertex at (-2, 12) and also goes through (1, -15).
Answers
y = 23.6(x + 2)² + 12 is the equation of the parabola with a vertex at (-2, 12) and also goes through (1, -15).
The vertex form equation of a parabola is,
y = a(x - h)² + k
where (h,k) is the vertex coordinates and an is a multiplier.
here (h,k) = (-2,12)
Taking, y = a(x - h)² + k
Substitute (1, -15) in the equation to derive.
(-15)² = a(1 - (-2))² + 12
225 = a(1 + 2)² + 12
225 - 12 = a(3)²
213 = a × 9
213 ÷ 9 = a
a = 23.6
The vertex form: y = 23.6(x + 2)² + 12
simplifying,
23.6 × (x² + 2 × x × 2 + 4) + 12
= 23.6 × (x² + 4x + 4) + 12
= 23.6x² + 94.4x + 94.4 + 12
= 23.6x² + 94.4x + 106.4
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The cost for renting a truck for one day is $19.95 and has a rate of$0.50 per mile. Write a function rule to model the cost of renting atruck for one day. Then evaluate the function for traveling 73 miles.
Answers
The cost of renting a truck for one day is $19.95 and has a rate of $0.50 per mile.
We can write a function rule to model the cost of renting a truck for one day.
[tex]y=0.50x+19.95[/tex]Where x is the number of miles and y is the corresponding cost of renting.
Now we can find the cost of renting for traveling 73 miles.
Substitute x = 73 into the function.
[tex]\begin{gathered} y=0.50(73)+19.95 \\ y=36.5+19.95 \\ y=\$56.45 \end{gathered}[/tex]Therefore, the cost of renting the truck for one day and 73 miles will be $56.45
i’m stuck on this question. any help would be greatly appreciated
Answers
Using the Pythagorean theorem we get:
[tex]y^2+8^2=12^2.[/tex]Simplifying the above result we get:
[tex]y^2+64=144.[/tex]Subtracting 64 from the above equation we get:
[tex]\begin{gathered} y^2+64-64=144-64, \\ y^2=80. \end{gathered}[/tex]Therefore:
[tex]y=\sqrt{80}\approx8.9.[/tex]Answer:
[tex]y=8.9.[/tex]What are the domain and the range of this function? please i need this fast ill give 15 pts
Answers
Given data:
The given graph is shown.
The domain is the value of x for which the given function is defined, the domain of the given graph is,
[tex]D=\lbrack-5,1)[/tex]The range is the value of y for which the given function is defined, the range of the given graph is,
[tex]R=\lbrack-4,\text{ 7)}[/tex]Thus, the domain of the given function is [-5,1), and range is [-4, 7).
what is 28m-35 in factored form?
Answers
Answer:
[tex]28m-35=7\mleft(4m-5\mright)[/tex]Explanation:
Given the expression:
28m - 35
To write this in factored form, note that
[tex]\begin{gathered} 28=7\times4 \\ \text{and} \\ 35=7\times5 \end{gathered}[/tex]So
[tex]28m-35=(7\times4m)-(7\times5)[/tex]Because 7 is common to both 28m and 35, we factor out 7, to have
[tex]7\mleft(4m-5\mright)[/tex]Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonadeis $8.00 and a small lemonade is $2.00.The expression represents 50% of the money he collects,0.50(8/ + 2)Use the Distributive Property to expand the expression.The simplified expression is
Answers
Based on the given information, you have the following expression:
0.50(8l + 2s)
by using distributive property, you obtain:
0.50(8l + 2s) = 0.50(8l) + 050(2s)
= 4l + s
Hence, the simplified expression is 4l + s
A right triangle has one leg twice as long as the other and the perimeter is 18. Find the three sides of the triangle. Draw a diagram.
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Let x represent the shortest leg of the triangle. If one leg twice as long as the other, then the length of the other leg is 2x.
Let y represent the hypotenuse which is the longest leg. The diagram is shown below
By applying pythagorean theorem,
y^2 = x^2 + (2x)^2
y^2 = x^2 + 4x^2 = 5x^2
Recall, perimeter of a triangle is the sum of the length of the sides of the triangle. If perimeter is 18, it means that
x + 2x + y = 18
3x + y = 18
y = 18 - 3x
Substituting y = 18 - 3x into y^2 = 5x^2, we have
(18 - 3x)^2 = 5x^2
324 - 54x - 54x + 9x^2 = 5x^2
9x^2 - 5x^2 - 54x - 54x + 324 = 0
4x^2 - 108x + 324 = 0
x^2 - 27x + 81 = 0
By applying the formula for quadratic equations, we have
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ x\text{ = }\frac{-\text{ - 27}\pm\sqrt[]{-27^2-4(1\times81)}}{2\times1} \\ x\text{ = }\frac{27\pm\sqrt[]{405}}{2} \\ x\text{ = }\frac{27\text{ + 20.12}}{2}\text{ or x = }\frac{27\text{ - 20.12}}{2} \\ x\text{ = 23.56 or x = 3.44} \end{gathered}[/tex]The sides would be
3.44
2 x 3.44 = 6.88
18 - 3(3.44) = 7.68
The three sides are 3.44, 6.88 and 7.68
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Zoe is making greeting cards, which she will sell by the box at an arts fair. She paid $22 for a booth at the fair, and the materials for each box of cards cost $4. She will sell the cards for $15 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take? How much will the sales and expenditures be?
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Let x be the number of box cards
Expenditures: $22 plus $4 times x
[tex]E=22+4x[/tex]Sales: $15 times x
[tex]S=15x[/tex]At some point, she will sell enough cards so that her sales of her cover her expenditures of her: Equal E and S
[tex]E=S[/tex]Substitute the values of E and S:
[tex]22+4x=15x[/tex]Solve x:
[tex]\begin{gathered} 22+4x-4x=15x-4x \\ 22=11x \\ \frac{22}{11}=\frac{11}{11}x \\ 2=x \\ \\ \\ x=2 \end{gathered}[/tex]Use the value of x to find the sales and expenditures:
[tex]\begin{gathered} S=15x \\ S=15(2) \\ S=30 \\ \\ E=22+4x \\ E=22+4(2) \\ E=22+8 \\ E=30 \end{gathered}[/tex]Then, It takes to Zoe sell 2 box cards to cover the expenditures, the sales need to be $30 to cover the expendituresEvaluate the following expression for P=8000, r=9%, k=4, and n=16.
Answers
Given expression:
[tex]p(1\text{ + }\frac{r}{k})^{kn}[/tex]We have :
p = 8000
r = 9%
k = 4
n = 16
Substituting into the given expression:
[tex]=\text{ 8000}\times\text{ (1 + }\frac{0.09}{4})^{4\times16}[/tex]Evaluating:
[tex]\begin{gathered} =\text{ 8000 }\times(1+0.0225)^{64} \\ =\text{ 8000 }\times(1.0225)^{64} \\ =\text{ 33230.91155} \\ \approx\text{ 33230.91} \end{gathered}[/tex]Answer: 33230.91
solve the formula for the specified variable
c=xy
solve for x
Answers
Answer: [tex]x= \frac{c}{y}[/tex]
Step-by-step explanation:
You want to isolate x on the right side ((x)=) This means making x alone.
To do so, you want to divide y on both sides. Division is the opposite of x.
[tex]\frac{c}{y}= \frac{xy}{y}[/tex]
The y's cancel out the right leaving:
[tex]\frac{c}{y} = x[/tex]
largest 5-digit number rounded
to the nearest 100?
Answers
Answer:
100000
Step-by-step explanation:
the largest five digit number is 99999
to round it to the nearest hundred you must look at the tens place to see if it is above or below 5
it is above 5 so your round up
because it is a nine it becomes 10
this goes down the line until you get
100000
that is your answer
Answer:
99,999
it is the answer!
a gardner has a cylindrical planter that has a diameter of 16 inches and is 2 feet deep. What is the approximate number od cubic feet of potting soil that he will need to fill the planter.
Answers
Given a cylinder with a diameter of d and a height of h, the volume, V, is given by
[tex]V=\frac{\pi d^2h}{4}[/tex]In this case,
d = 16 inches, h = 2ft
1 foot = 12 inches
Therefore,
[tex]d=\frac{16}{12}=\frac{4}{3}ft[/tex]Therefore,
[tex]V=\frac{\pi(\frac{4}{3})^22}{4}=\frac{\pi(4)(2)}{3^2}=\frac{8\pi}{9}\text{ cubic fe}et[/tex]V=2.79 cubic feet
Therefore the approximate number is 2.79
Which of the following is the once of a rhombus?
Product of its diagonals.
Half of sum of its diagonals
Half of product of its diagonals.
Answers
The answer is Half of product of its diagonals which is option C .
Let d1 and d2 be the diagonals of the rhombus.
A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square. That is why it is also known as a tilted square.
Area of rhombus using diagonals (A) = 1/2 * d1 * d2.
where ,
d1 = length of diagonal 1
d2 = length of diagonal 2.
Therefore the answer is Half of product of its diagonals which is option C.
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helppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
8, 11, 10
Step-by-step explanation:
Choose all the equations that have p = -(1/4) as the solution.A.) 3p + 2 = 5/4B.) 5p - 2 = 3/4 C.) 3p - 2 = 5/4 D.) 5p + 2 = 3/4
Answers
EXPLANATION
Given the equations in the problem, we just need to replace each p-term by -1/4 in order to see if this is a solution to each equation:
A.) 3*(-1/4) +2 = 5/4 = 5/4 --------> p = -(1/4) is a solution of this equation. ✔✔
B.) 5*(-1/4) - 2 = -13/4 ≠ 3/4 -------> p = -(1/4) is NOT a solution of this equation.✘✘
C.) 3*(-1/4) -2 = -11/4 ≠ 5/4 -------> p = -(1/4) is NOT a solution of this equation.✘✘
D.) 5*(-1/4) +2 = -11/4 ≠ 5/4 -------> p = -(1/4) is NOT a solution of this equation.✘✘
Mayor has 20 prizes. He decided to give 1/2 to the relay game. How many of the prizes are for the relay games?
Answers
The total is 20 prizes. If he gives one half of them to the relay games, then the number of prizes for the relay games are 10 (it's 20 divided by 2)
Answer:
Step-by-step explanation:
10
one half of 20 is 10.
17. Points W and Z are 8 unitsapart on the coordinate grid. Four facts aboutthe coordinates of the points are shown.• Point W is located at (-3, p).• The variable p has a value greater than 0.• Point Z is located at (-3, r).• The variable r has a value less than 0.What are possible values of p and r?p=OOlolOOO OCOOOOOOOOOOOOOSOOCOOOOOOOOOO0 0 0 0OOOOOOOCCO0 0
Answers
Possible values of p are from 1 to 7 while possible values of r are from -1 to -7
Here, we want to get the possible values of p and r
From the question, we have it that both W and Z are located at the same axis coordinate
What this mean is that it is a vertical line that connects both
Variable p has a value greater than zero means that it has a positive value
Variable r has a value less than zero means it has a negative value
Since the two are 8 units apart, we have it that;
p-r = 8
or p = 8 + r
Also, we have it that;
p > 0
r < 0
So, we need pairs of numbers that could work
We can use different values, minding the fact that p is positive and r is negative
If we have p = 7
r will be 7-8 = -1
p = 7 and r = -1 is a possible value
p = 6 and r = -2 is a possible value
p = 5 and r = -3 is a possible value
p = 4 and r = -4 is a possible value
p = 3 and r = -5 is a possible value
p = 2 and r = -6 is a possible value
p = 1 and r = -7 is a possible value
Thus, we have it that the value of p ranges from 1 to 7 while the value of r ranges from -1 to -7
Which is an x-intercept of the graphed function?
O (0, 4)
(-1, 0)
(4, 0)
(0, -1)
Answers
A line's x-intercept and y-intercept are the points at which the x axes- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.
We set y = 0 and solve the equation for x to determine the x-intercept.
The graphed function derived from the choices has the x-intercept (-1, 0)
How do you calculate the x-intercept?A graph's x-intercept is the location where the graph crosses the x-axis.
The graph in the accompanying image crosses the x-axis at:
(-2, 0), (-1, 0), (1, 0) and (2, 0) (2, 0)
Consequently, the x-intercept of the graphed function derived from the alternatives (-1, 0)
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It’s asking to find / solve for X. I just can’t remember how to do it
Answers
Given:
There are given that arc length is 192 degrees and angle G is:
[tex]31x+3[/tex]Explanation:
To find the value of x, we need to use the circle properties:
So,
From the circle properties:
[tex]31x+3=192^{\circ}[/tex]Then,
Subtract 3 from both sides of the equation:
So,
[tex]\begin{gathered} 31x+3=192^ \\ 31x+3-3=192^-3 \\ 31x=189 \end{gathered}[/tex]Now,
Divide by 31 on both sides of the above equation:
So,
[tex]\begin{gathered} 31x=189 \\ x=\frac{189}{31} \\ x=6.096 \end{gathered}[/tex]Final answer:
Hence, the value of x is shown below:
[tex]x=6.096[/tex]Can you prove these triangles are congruent from the information given?
Answers
Given:
Give names to the triangles
Aim:
We need to find whether these triangles are congruent.
Explanation:
The lines AE and DC are perbenticular.
[tex]\angle ABC\cong\angle\angle DBE\text{ since perpendicular lines makes right angles.}[/tex]Recall that the dashes on the lines show they are equal in length.
[tex]BC\cong BD\text{ Since both sides have single dashes.}[/tex][tex]AC\cong DE\text{ Since both sides have double dashes.}[/tex]Two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.
[tex]\Delta ABC\cong\Delta DBE\text{ by SSA postulates}[/tex]Final answer:
The triangles ABC and DBE are congruent.
I need to use factorials and doing it step-by-step for the bio normal probability formula Please help me figure this A through C step-by-step they want the factorial symbol! When showing my workGiven the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)n = 15, p = 0.4, find P(4 successes) n = 12, p = 0.2, find P(2 success ) n = 20, p = 0.05, find P(at most 3 successes) (hint for c. P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)I just got disconnected from my tutor who said it would take 20 minutes to song and help me go over it step-by-step so if you were that tutor or any tour available please contact
Answers
Binomial distribution formula:
[tex]P(x)=\frac{n!}{(n-x)!x!}*p^x*q^{n-x}[/tex]________
n = 15, p = 0.4, find P(4 successes)
[tex]\begin{gathered} n=15 \\ x=4 \\ p=0.4 \\ q=1-0.4=0.6 \\ \\ P(x=4)=\frac{15!}{(15-4)!*4!}*0.4^4*0.6^{15-4} \\ \\ P(x=4)=\frac{15!}{11!*4!}*0.4^4*0.6^{11} \\ \\ P(x=4)=\frac{15\times14\times13\times12\times11!}{11!*4!}*0.4^4*0.6^{11} \\ \\ P(x=4)=\frac{15\times14\times13\times12}{4\times3\times2\times1}*0.4^4*0.6^{11} \\ \\ P(x=4)=1365*0.4^4*0.6^{11} \\ \\ P(x=4)=0.1268 \end{gathered}[/tex]__________________
n = 12, p = 0.2, find P(2 success )
[tex]\begin{gathered} n=12 \\ x=2 \\ p=0.2 \\ q=1-0.2=0.8 \\ \\ P(x=2)=\frac{12!}{(12-2)!*2!}*0.2^2*0.8^{12-2} \\ \\ P(x=2)=\frac{12!}{10!*2!}*0.2^2*0.8^{10} \\ \\ P(x=2)=\frac{12\times11\times10!}{10!*2!}*0.2^2*0.8^{10} \\ \\ P(x=2)=\frac{12\times11}{2\times1}*0.2^2*0.8^{10} \\ \\ P(x=2)=66*0.2^2*0.8^{10} \\ \\ P(x=2)=0.2835 \end{gathered}[/tex]_________________________
n = 20, p = 0.05, find P(at most 3 successes)
Find each part (P(x=0), P(x=1), P(x=2), P(x=3)) and then sum the results
[tex]\begin{gathered} n=20 \\ p=0.05 \\ q=1-0.05=0.95 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} P(x=0)=\frac{20!}{(20-0)!0!}*0.05^0*0.95^{20-0} \\ \\ P(x=0)=\frac{20!}{20!*0!}*1*0.95^{20} \\ \\ P(x=0)=\frac{20!}{20!*1}*1*0.95^{20} \\ P(x=0)=1*1*0.95^{20} \\ P(x=0)=0.3585 \end{gathered}[/tex][tex]\begin{gathered} P(x=1)=\frac{20!}{19!*1!}*0.05^1*0.95^{19} \\ \\ P(x=1)=\frac{20\times19!}{19!*1}*0.05*0.95^{19} \\ \\ P(x=1)=20*0.05*0.95^{19} \\ P(x=1)=0.3774 \\ \end{gathered}[/tex][tex]\begin{gathered} P(x=2)=\frac{20!}{18!*2!}*0.05^2*0.95^{18} \\ \\ P(x=2)=\frac{20\times19\times18!}{18!*2\times1}*0.05^2*0.95^{18} \\ \\ P(x=2)=190*0.05^2*0.95^{18} \\ P(x=2)=0.1887 \end{gathered}[/tex][tex]\begin{gathered} P(x=3)=\frac{20!}{17!*3!}*0.05^3*0.95^{17} \\ \\ P(x=3)=\frac{20\times19\times18\times17!}{17!*3\times2\times1}*0.05^3*0.95^{17} \\ \\ P(x=3)=1140*0.05^3*0.95^{17} \\ P(x=3)=0.0596 \end{gathered}[/tex][tex]P(x\leq3)=0.3585+0.3774+0.1887+0.0596=0.9842[/tex]A box of cereal states that there are 81 calories in a
3/4-cup serving. What is the unit rate for calories per cup? How many calories are there in of the cereal?
Answers
27 * 4 = 108
Answer= 108
Ava has 6 boxes of supplies for her classroom each box has a mass of 4 kg what is the total mass for all boxes
Answers
Given the mass of each box, and the total number of boxes, multiply both quantities to obtain the total mass, as shown below
[tex]6\cdot4=24\to6\text{ boxes, 4 }kg\text{ each}[/tex]Therefore, the answer is 24kg.
A recipe calls for 3/4 cup sugar if the recipe is divided by 3 how much sugar is needed
Answers
Answer:
It'd be 1/4 a cup of sugar.
Step-by-step explanation:
Take 3/4 and divide it by 3/4 and because the denominator is the same, the top numbers divide each other and since 3 is divided by 3 is 1, you get the answer of 1/4 and then you can do that to all the other ingredients in the recipe.
